It appears to be easier for a woman to get elected to the U.S. Senate than it is for her direct a Broadway play. Twenty percent of those making up the prestigious government body currently have X and Y chromosomes, but in the past decade, no more than 18% of the directors of Tony-eligible productions have been female.

However, as this season begins, the Great Male White Way is getting a stronger shot of estrogen with four females quarterbacking productions. Two of the most heralded shows boast women directors. The Curious Incident of the Dog in the Night-Time is led by Tony-winner Marianne Elliott, who turned the London production into a smash hit. And Pam MacKinnon, who won a Tony for directing Edward Albee's Who's Afraid of Virginia Woolf?, is bringing a star-studded revival of his A Delicate Balance to the stage.

Meanwhile, Kimberly Senior is reprising her role as director of the Pulitzer Prize-winning play Disgraced, which wowed audiences at Lincoln Center's Claire Tow Theater, and Tony winner Anna Shapiro is at the helm of This Is Our Youth, which is coming to New York after an acclaimed run at Chicago's Steppenwolf Theatre.

These four are staging 33% of the 12 Tony-eligible shows, according to the most recent data available from the Stage Directors and Choreographers Society, or SDC, a union. Of course, women directors still have a long way to go to reach parity. Only eight women have ever won a Tony for directing.

Many in the wings

"I try to stay optimistic, but the numbers are terrible," said Leigh Silverman, an SDC vice president who was nominated for a Tony last season for directing Violet. "Maybe this is the start of change."

There has been some minor improvement. Last season, 13% of Tony-eligible productions were directed by women, up from 5% a decade ago. In 2013, women won both the Tony for directing a play and for directing a musical.

There's a dearth of female directors on Broadway for the same reasons that women trail men in leadership roles in other industries. It's tough to crack the male power base, especially when women are spending more time raising children. Even this season, the percentage of women directors is likely to move lower as more shows open.

"People keep asking me who is taking care of my kids," said Ms. Senior, a mother of two who is based in Chicago. "Can you imagine anyone asking that to a man?" A native of Short Hills, N.J., Ms. Senior grew up attending Broadway shows, but relocated to Chicago because she knew it would be hard, if not impossible, to launch a directing career on the world's biggest stage. She's directed more than 100 plays in regional theaters, but is making her Broadway debut with Disgraced, which was initially staged in Chicago before moving to Lincoln Center.

Disgraced marks a milestone for one of its producers as well. It is the first time the Araca Group has backed a Broadway show directed by a woman, although it has financed female-led productions elsewhere. It's a distinction that Michael Rego, an Araca founder and partner, didn't realize until a reporter asked about it. "I think you are trying to find the best person for the job," he said.

Mr. Rego concedes that many years ago a woman told him she believed his short list of favorite directors was composed exclusively of men. He said that wasn't true, but was bothered by the impression, so he widened his circle to include more women.

Establishing relationships with key producers and writers is crucial for a director's career. Ms. Senior directed Disgraced author Ayad Akhtar's most recent play, The Who and the What, which ran earlier this year at Lincoln Center. Ms. MacKinnon, at the suggestion of her agent, met Mr. Albee years ago over lunch, and is now directing one of his three Pulitzer Prize winners.

Mr. Rego noted it is expensive to stage Broadway productions, so personal connections are nearly as important as talent. It costs about $3 million to stage a straight play and upward of $8 million for a musical. "With that kind of money, you aren't going to trust just anyone," he said.

Three of the women currently slated to direct are Tony winners, so they are a proven commodity. Some female directors say the pressure on them to direct hits is magnified because there are so few of them. "I think that we are more in the spotlight," said Ms. Elliott. "We are judged more harshly."

Still, she banishes those thoughts when choosing what to direct. Curious Incident wasn't an obvious hit. It is the story of an autistic boy who searches for the killer of his neighbor's dog. But Ms. Elliott said she was especially touched by the boy's parents in the play, who keep trying and failing to help him. The show won seven Olivier Awards, the British equivalent of the Tony, including one for her.

Taming of a shrew

Female directors say it's impossible to judge how their gender affects their work since it is a part of them, like their race, religion, age and background. Yet, Ms. Senior said that gender has governed some of her choices. For a long time she shunned feminist-themed plays because she didn't want to be pigeonholed as a "female director." Now that she's established and more confident, she doesn't worry about such matters.

Ms. MacKinnon said she believes her gender may have subtly affected how the character Martha was portrayed in her recent staging of Who's Afraid of Virginia Woolf? Martha is generally considered a shrew in the play about her disintegrating marriage to husband George.

"I loved Martha," said Ms. MacKinnon. "I really hooked into her loneliness and the love that there was between Martha and George, and maybe that's because I'm a woman."

Her critically hailed direction won her a Tony, admitting her to a very exclusive club.